What are the divisors of 9120?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 19, 20, 24, 30, 32, 38, 40, 48, 57, 60, 76, 80, 95, 96, 114, 120, 152, 160, 190, 228, 240, 285, 304, 380, 456, 480, 570, 608, 760, 912, 1140, 1520, 1824, 2280, 3040, 4560, 9120

There is a total of 48 positive divisors.
The sum of these divisors is 30240.
The arithmetic mean is 630.

40 even divisors

2, 4, 6, 8, 10, 12, 16, 20, 24, 30, 32, 38, 40, 48, 60, 76, 80, 96, 114, 120, 152, 160, 190, 228, 240, 304, 380, 456, 480, 570, 608, 760, 912, 1140, 1520, 1824, 2280, 3040, 4560, 9120

8 odd divisors

1, 3, 5, 15, 19, 57, 95, 285

How to compute the divisors of 9120?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 9120 by each of the numbers from 1 to 9120 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

9120 / 1 = 9120 (the remainder is 0, so 1 is a divisor of 9120)
9120 / 2 = 4560 (the remainder is 0, so 2 is a divisor of 9120)
9120 / 3 = 3040 (the remainder is 0, so 3 is a divisor of 9120)
...
9120 / 9119 = 1.0001096611471 (the remainder is 1, so 9119 is not a divisor of 9120)
9120 / 9120 = 1 (the remainder is 0, so 9120 is a divisor of 9120)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 9120 (i.e. 95.498691090507). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

9120 / 1 = 9120 (the remainder is 0, so 1 and 9120 are divisors of 9120)
9120 / 2 = 4560 (the remainder is 0, so 2 and 4560 are divisors of 9120)
9120 / 3 = 3040 (the remainder is 0, so 3 and 3040 are divisors of 9120)
...
9120 / 94 = 97.021276595745 (the remainder is 2, so 94 is not a divisor of 9120)
9120 / 95 = 96 (the remainder is 0, so 95 and 96 are divisors of 9120)